Problem: Find all $x$ such that $x^2+5x<6$. Express your answer in interval notation.
Explanation: Subtracting 6 from both sides of the equation, we get the quadratic  \begin{align*} x^2+5x-6&<0 \quad \Rightarrow
\\ (x+6)(x-1)&<0.
\end{align*} Since -6 and 1 are both roots of the quadratic, the inequality changes signs at these two points. So, we need to test the signs of three ranges of numbers: $x<-6$, $-6<x<1$, $x>1$. When $x<-6$, both $(x+6)$ and $(x-1)$ will be negative, thus making the inequality positive. When $-6<x<1$, only $(x-1)$ will be negative, thus making the inequality negative. Finally when $x>1$, both $(x+6)$ and $(x-1)$ will be positive, thus making the inequality positive once again. Therefore, the only range of $x$ that satisfies the inequality is $\boxed{(-6, 1)}$.